Freezing point depression
Freezing point depression FPDF or Anti Freezing Power AFP or Potere Anti-Congelante PAC is the lowering of the freezing point of water. When making ice cream this can be used to predict the softness or scoopability at a certain serving temperature. This is especially important in ice cream display cabinets where all the different flavored ice creams must have the same softness. The main ingredients that suppresses the freezing point is SUGAR, SALT and ALCOHOL. You have probably seen in many recipes that you can add a splash of alcohol or a little salt to make the ice cream softer. But the most important ingredient is sugar. By using different types of sugars you can control the sweetness and freezing point of your ice cream. If your ice cream is too hard but has the correct sweetness you can’t just add more sucrose to make it softer you have to use a mix of different sugars.
The freezing point depression in itself is a hint of how soft the ice cream will be, there are other factors to consider as well. If everything else is equal the ice cream with the highest PAC value will be softer. When we calculate the PAC in relation to the water content and look at the freezing curve we get a better measurement of softness.
Science
The science behind freezing point depression is related to the molecular weight of an ingredient. Normal table sugar SUCROSE has a molecular weight of 342 and is used as a reference when calculating PAC.
100g of sucrose in 1000g of water has a PAC of 100
Other types of sugars have different molecular weights and thus affects the freezing point differently. What we do is to calculate the Sucrose Equivalent of any other sugar.
Implementation details
This section is an explanation of how PAC is implemented in the software. There is not a standard way of calculating this. Different sources calculate the PAC and FP in different ways and in different detail. My approach is like this. I calculate the PAC for sugars (PACse or PAC sucrose Equivalent) and use experimental data tables for sucrose solutions to calculate the FP. I then separately calculate the FP for salt, alcohol and for the salts in MSNF. These FPs are then added together to find the final FP. Alternative ways would be to sum the PAC from sugars, salts, alcohol and salts in MSNF to get one final PAC and either use the sucrose table to find the FP or use the linear formula for freezing point depression. So, if you look at other calculators or sources for PAC and freezing point calculations be aware that they might differ from my software both due to different calculations and also of course how the PAC is defined for the ingredients.
Sugars
The most useful sugars in home ice cream making are sucrose, dextrose and fructose. These are all in powder form and is easy to measure and work with. Honey, glucose syrup and other syrups are also common. Lactose is the sugar in milk and also affects the freezing point.
| Sugar | PAC | Relative sweetness POD |
| Sucrose | 100 | 100 |
| Dextrose | 190 | 70 |
| Fructose | 190 | 170 |
| Glucose syrup (DE42) | 80 | 50 |
| Honey | 146 | 75 |
| Lactose | 100 | 16 |
| Salt* | 585 | 0 |
| Alcohol* | 740 | 0 |
Example
To illustrate assume we have the following ingredients.
Water 800g
Sucrose 200g
PAC 200
POD 200
The PAC will be 200 and the POD (relative sweetness) will also be 200. Now we want to keep the relative sweetness and raise the PAC. We can replace some of the sugar with dextrose to accomplish this. Since dextrose only have 70% sweetness compared to sucrose we also need to reduce the water to get the same sweetness.
Water 784g
Sucrose 162g
Dextrose 54g
PAC 265
POD 200
So, by replacing some of the sucrose with dextrose we have kept the sweetness the same but increased the PAC making the ice cream softer.
If we use fructose as well we can use dextrose+fructose to get the same sweetness as sucrose.
Water 800g
Sucrose 150g
Dextrose 35g
Fructose 15g
PAC 245
POD 200
So, we can use a blend of sugars to manipulate the sweetness and the freezing point depression of our ice cream.
Freezing point
All water does not freeze at the same time. Using the PAC we can calculate when the water starts to freeze. This is called the freezing point or FP. So at the FP we have 0% frozen water. When water starts to freeze the concentration of the sugars increases resulting in a higher PAC for the remaining water. Thus we need lower temperatures to freeze more water and so on. This is also the reason why your ice cream machine can not freeze your ice cream completely.
To calculate the freezing point for sugars I use a table of experimental data of sucrose solutions. For salt and alcohol I use a linear formula based on the molality of salt and alcohol.
Freezing curve
Adding the freezing point for the sugars, salt and alcohol we get the initial freezing point of the ice cream. By simulating more and more water being frozen we can plot a freezing curve. This curve can then be used to calculate the serving temperature of the ice cream or indicate how much water is frozen at a certain temperature. I try to aim for approx 75% frozen water at -14C.
Thanks for the good explanation.
Just a question for understanding the example: 800g water with 200g sucrose will give a PAC of 200g sucrose/800g water*1000=250 for me instead of 200 as written in the article. Or am I on the wrong path? The calculation of @gelatologist in the medium article seems to have the same issue.
Any feedback would be great.
https://medium.com/@ciao_86520/what-pac-is-and-how-to-calculate-it-2f1ade1bd5df
It is calculated as sucrose/(water+sucrose) so you get
200/(200+800)=0.2
This is how the pac is calculated in all calculators or books I have seen. I actually tried to change the calculations once to use the concentration but the freezing curves will not be correct.
Hi Patrick,I’m looking for a type of sugar that is sweet but don’t provide much anti freezing effect because I want to increase the amount of liquor in my ice cream without compensating its sweetness. I mean the POD/PAC ratio should be lower than 1 because sucrose, dextrose, fructose and maltodextrin just don’t work. I’ve used artificial sweetener such as sucralose and the result was good but I still don’t want to use artificial sweetener. Thanks in advance
Hi,
Unfortunately all of the normal sugars that are sweeter than sucrose also have a high PAC.
And all sugar alcohols are less sweet than sugar and have higher or equal PAC to sucrose.
So, that leaves you with the high intensity sweeteners like Sucralose, Stevia, Aspartame etc…
I haven’t done much on this type of ice creams but I think the only alternative is to find a high intensity sweetener and then compensate the lack of solids with some fiber like Inulin.
Maybe there is a sugar out there that is sweeter than sucrose but have a lower PAC, that would be great but I don’t know about it.
Good Luck.
I chose to use maltodextrin to increase the solid and sucralose for sweetness but if one of my customers found out that the sweetness of his ice cream was very weird so I decided to stop using sucralose. Some professionals told me to use monk fruit but I haven’t had the technical data. Making liquor ice cream seems to be very hard
I have used a 10% replacement of sugar with vegetable fiber (inulin) and an addition of .1% (yes POINT one %) gum Arabic by total mass to be frozen where the base was 3.125% ethanol. May not seem like much, but that is 2 btls 1500ml of 12% wine in a 5 lt batch of base, basically frozen Spritz with no weeping while kept in 10ºF (-12ºC) dipping cabinet for service of 8 hrs. Firm enough to serve in a cone.
No precooking of alcohol.
Hello dear,
I’m trying to lower my POD value and increase the Solid content
I am intending to use Glucose powder DE 21 does it affect the taste of ice cream ?
Thank you in advance
No it should not affect the taste.
Hello, can you explain me the difference between PACse and PACnormalized? I don’t know how to understand what it stand for and how to interpret (PAcnormalized) final result. Thanks
Ok, PACnormalized is the PAC/Water. So it is the PAC in the water part of the mix.
I usually think of it as the concentration of sugars in the water.
This is a very good explanation of PAC and normalized PAC
https://medium.com/@gelatologist/how-hard-to-scoop-will-my-gelato-be-part-i-332a76e6cb8f
Thanks, now that make a lot of sense 🙂
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